91Ó°ÊÓ

Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. $$ y=-x^{4}+3 x^{2}-1 $$

Describe the \(x\) -values at which the function is differentiable. Explain your reasoning. $$ y=(x-3)^{2 / 3} $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$y=-\frac{4}{(t+2)^{2}}$$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=\frac{3}{\left(x^{3}-4\right)^{2}} $$

Describe the \(x\) -values at which the function is differentiable. Explain your reasoning. $$ y=x^{2 / 5} $$

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. $$ \text { If } y=(x+1)(x+2)(x+3)(x+4), \text { then } \frac{d^{5} y}{d x^{5}}=0 $$

Determine the point(s), if any, at which the graph of the function has a horizontal tangent line. $$ y=x^{3}+3 x^{2} $$

Use a graphing utility to graph \(f\) and \(f^{\prime}\) on the interval \([-2,2] .\) $$ f(x)=x^{2}(x+1)(x-1) $$

Describe the \(x\) -values at which the function is differentiable. Explain your reasoning. $$ y=\sqrt{x-1} $$

determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f^{\prime}(c)\) and \(g^{\prime}(c)\) are zero and \(h(x)=f(x) g(x),\) then \(h^{\prime}(c)=0\)